Berezhnyi M. Homogenized models of complex fluids

Objects: System of equations modelling the dynamics of complex fluids consisting of a viscous incompressible fluid (dispersion medium) and a large number of small solid particles (dispersive medium) suspended in the fluid. Subjects: The asymptotic behavior of solutions of boundary-value problems describing small non-stationary oscillations of complex fluids, and behavior of convergence to solutions of the homogenized systems of equations. Methods: Variational methods of homogenization, methods of functional analysis and theory of functions of complex variable, methods of spectral theory of operator sheaves. New theoretical results: Derivation of macroscopic (homogenized) models of complex fluids under various relations between the parameters describing the microstructure of the fluids. It is shown that, depending on this relation, the homogenized models are qualitatively different ones. For the specific microstructure all the homogenized models are found in explicit form. Employment: The results are important both for qualitative and for quantitative analysis of physical processes in complex fluids.